Check bulletin boards at local coffee shops, music stores or music venues. Local bands usually have very limited advertising budgets, so they will advertise on flyers that they can post for free.
Check websites for local music venues, radio stations or sites like Myspace.com or LocalBandNetwork.com. These sites will advertise local shows, and sites like Myspace.com allow bands to create profiles that showcase their music and concert schedules.
Ask around your city about lesser-known venues and bands. One of the best ways to find out about a band and the group's talent is by word of mouth. Talk to people who have similar music taste to you and ask if they have any recommendations for local bands.
Go to concerts of more widely known bands in your city. Bigger bands will often have smaller, local bands open for them, which is a great way to find new music.